Prove that `sin 20^(@) sin 40^(@) sin 80^(@) = (sqrt3)/(8).`

Prove that sin20^(@)sin40^(@)sin80^(@)=(sqrt(3))/(8)

Prove that cos 20^(@) cos 40^(@) cos 80^(@) = (1)/(8).

Prove that sin ^(2) 72 ^(@)- sin ^(2) 60 ^(@)= (sqrt5-1)/(8).

Prove that : sin 10^(@) + sin 20^(@) + sin 40^(@) + sin 50^(@) = sin 70^(@) + sin 80^(@).

Prove that: cos20^(@)cos40^(@)cos80^(@)=1/8

sin ^(2) 24 ^(@) - sin ^(2) 6^(@) = (sqrt5 -1)/(8).

Prove that: i) sin20^(@)sin40^(@)sin60^(@)sin80^(@)=3/16 ii) sin10^(@)sin50^(@)sin60^(@)sin70^(@)=sqrt(3)/16 iii) sin20^(@)sin40^(@)sin80^(@)=sqrt(3)/8

Prove that: sin20^0sin40^0sin80^0=(sqrt(3))/8

Prove that (sin20^(@) + sin40^(@)) + (cos20^(@) + cos40^(@))=(sqrt(3)+1)cos10^(@)

Prove that : sin^2(72^@) - sin^2 (60^@) = (sqrt5 - 1)/8